/* nag_dggsvp (f08vec) Example Program. * * Copyright 2011 Numerical Algorithms Group. * * Mark 23, 2011. */ #include #include #include #include #include #include #include int main(void) { /* Scalars */ double eps, norm, tola, tolb; Integer i, irank, j, k, l, m, n, nrows, p, pda, pdb, pdq, pdu, pdv; Integer exit_status = 0; /* Arrays */ double *a = 0, *b = 0, *q = 0, *u = 0, *v = 0; /* Nag Types */ NagError fail; Nag_OrderType order; #ifdef NAG_COLUMN_MAJOR #define A(I, J) a[(J-1)*pda + I - 1] #define B(I, J) b[(J-1)*pdb + I - 1] order = Nag_ColMajor; #else #define A(I, J) a[(I-1)*pda + J - 1] #define B(I, J) b[(I-1)*pdb + J - 1] order = Nag_RowMajor; #endif INIT_FAIL(fail); printf("nag_dggsvp (f08vec) Example Program Results\n\n"); /* Skip heading in data file */ scanf("%*[^\n]"); scanf("%ld%ld%ld%*[^\n]", &m, &n, &p); if (n < 0 || m < 0 || p < 0) { printf("Invalid n, m or p\n"); exit_status = 1; goto END; } #ifdef NAG_COLUMN_MAJOR pda = m; pdb = p; pdv = p; #else pda = n; pdb = n; pdv = m; #endif pdq = n; pdu = m; /* Allocate memory */ if (!(a = NAG_ALLOC(m*n, double)) || !(b = NAG_ALLOC(p*n, double)) || !(q = NAG_ALLOC(n*n, double)) || !(u = NAG_ALLOC(m*m, double)) || !(v = NAG_ALLOC(p*m, double))) { printf("Allocation failure\n"); exit_status = -1; goto END; } /* Read the m by n matrix A and p by n matrix B from data file */ for (i = 1; i <= m; ++i) for (j = 1; j <= n; ++j) scanf("%lf", &A(i, j)); scanf("%*[^\n]"); for (i = 1; i <= p; ++i) for (j = 1; j <= n; ++j) scanf("%lf", &B(i, j)); scanf("%*[^\n]"); /* get norms of A and B using nag_dge_norm (f16rac). */ nag_dge_norm(order, Nag_OneNorm, m, n, a, pda, &norm, &fail); nag_dge_norm(order, Nag_OneNorm, p, n, b, pdb, &norm, &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_dge_norm (f16rac).\n%s\n", fail.message); exit_status = 1; goto END; } /* Get the machine precision, using nag_machine_precision (x02ajc) */ eps = nag_machine_precision; tola = MAX(m, n) * norm * eps; tolb = MAX(p, n) * norm * eps; /* Compute the factorization of (A, B) (A = U*S*(Q**T), B = V*T*(Q**T)) * using nag_dggsvp (f08vec). */ nag_dggsvp(order, Nag_AllU, Nag_ComputeV, Nag_ComputeQ, m, p, n, a, pda, b, pdb, tola, tolb, &k, &l, u, pdu, v, pdv, q, pdq, &fail); if (fail.code != NE_NOERROR) { printf("Error from nag_dggsvp (f08vec).\n%s\n", fail.message); exit_status = 1; goto END; } /* Print details of the generalizeed SVD */ irank = k + l; printf("Numerical rank of (A**T B**T)**T (K+L)\n%5ld\n\n", irank); nrows = MIN(m,irank); fflush(stdout); nag_gen_real_mat_print_comp(order, Nag_UpperMatrix, Nag_NonUnitDiag, nrows, irank, &A(1, n - irank + 1), pda, "%13.4e", "Matrix S", Nag_IntegerLabels, 0, Nag_IntegerLabels, 0, 80, 0, 0, &fail); if (fail.code != NE_NOERROR) goto FAIL; printf("\n"); fflush(stdout); nag_gen_real_mat_print_comp(order, Nag_UpperMatrix, Nag_NonUnitDiag, l, l, &B(1, n - l + 1), pdb, "%13.4e", "Upper triangular matrix T", Nag_IntegerLabels, 0, Nag_IntegerLabels, 0, 80, 0, 0, &fail); if (fail.code != NE_NOERROR) goto FAIL; printf("\n"); fflush(stdout); nag_gen_real_mat_print_comp(order, Nag_GeneralMatrix, Nag_NonUnitDiag, m, m, u, pdu, "%13.4e", "Orthogonal matrix U", Nag_IntegerLabels, 0, Nag_IntegerLabels, 0, 80, 0, 0, &fail); if (fail.code != NE_NOERROR) goto FAIL; printf("\n"); fflush(stdout); nag_gen_real_mat_print_comp(order, Nag_GeneralMatrix, Nag_NonUnitDiag, p, p, v, pdv, "%13.4e", "Orthogonal matrix V", Nag_IntegerLabels, 0, Nag_IntegerLabels, 0, 80, 0, 0, &fail); if (fail.code != NE_NOERROR) goto FAIL; printf("\n"); fflush(stdout); nag_gen_real_mat_print_comp(order, Nag_GeneralMatrix, Nag_NonUnitDiag, n, n, q, pdq, "%13.4e", "Orthogonal matrix Q", Nag_IntegerLabels, 0, Nag_IntegerLabels, 0, 80, 0, 0, &fail); FAIL: if (fail.code != NE_NOERROR) { printf("Error from nag_gen_real_mat_print_comp (x04cbc).\n%s\n", fail.message); exit_status = 1; goto END; } END: if (a) NAG_FREE(a); if (b) NAG_FREE(b); if (q) NAG_FREE(q); if (u) NAG_FREE(u); if (v) NAG_FREE(v); return exit_status; }